Direct Visualization of Trimerized States in 1T0-TaTe2

Ismail El Baggari,1 Nikhil Sivadas ,2 Gregory M. Stiehl,1 Jacob Waelder,3 Daniel C. Ralph,1,4

Craig J. Fennie,2 and Lena F. Kourkoutis2,4,*1Department of Physics, Cornell University, Ithaca, New York 14853, USA

2School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA3Platform for the Accelerated Realization, Analysis and Discovery of Interface Materials (PARADIM),

Cornell University, Ithaca, New York 14853, USA4Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA

(Received 25 March 2020; revised 3 June 2020; accepted 26 August 2020; published 13 October 2020)

Transition-metal dichalcogenides containing tellurium anions show remarkable charge-lattice modulatedstructures and prominent interlayer character. Using cryogenic scanning transmission electron microscopy(STEM), we map the atomic-scale structures of the high temperature (HT) and low temperature (LT)modulated phases in 1T 0-TaTe2. At HT, we directly show in-plane metal distortions which form trimerizedclusters and staggered, three-layer stacking. In the LT phase at 93 K, we visualize an additionaltrimerization of Ta sites and subtle distortions of Te sites by extracting structural information from contrastmodulations in plan-view STEM data. Coupled with density functional theory calculations and imagesimulations, this approach opens the door for atomic-scale visualizations of low temperature phasetransitions and complex displacements in a variety of layered systems.

DOI: 10.1103/PhysRevLett.125.165302

Many layered transition-metal dichalcogenides (TMDs)undergo symmetry-breaking phase transitions by spatiallymodulating their electronic and structural degrees offreedom. The modulations may take the form of chargedensity waves (CDWs) and concomitant periodic latticedisplacements (PLDs) or polymerization of metal sites intoone-dimensional (1D) chain structures [1]. These broken-symmetry states couple strongly to electronic behavior,mediating for instance superconductivity or metal-insulatortransitions [2–4]. Modulated systems also exhibit richstructural complexity whereby the PLD patterns andperiodicities vary with the valence of the compound orby external parameters such as temperature and pressure[1,5]. Somewell-known superstructures include

ffiffiffiffiffi

13p

×ffiffiffiffiffi

13p

clustering in 1T-TaS2 and 1T-TaSe2, 3 × 3 in 2H-TaSe2,and 2 × 2 × 2 in 1T-TiSe2 [1].Compared to sulfides or selenides, tellurium-based

compounds (MTe2, M ¼ V, Nb, Ta, Ir) exhibit distinctelectronic and structural features including covalent Te-Tebonds between the layers, enhanced charge transfer to themetal sites, and significant in-plane electronic and struc-tural anisotropy [5–10]. MTe2 compounds hosting modu-lated phases at low temperature thus contain complex

interactions between in-plane and out-of-plane orderingtendencies. In IrTe2, for instance, the low temperaturephase involves the formation of in-plane Ir-Ir dimers anddistortions in interlayer Te bonding [11–14].The related 1T 0-TaTe2 has a distorted, monoclinic struc-

ture with space groupC2=m at high temperatures [9,15,16].The metal atoms form trimerized clusters with short bonds,which are also known as ribbon-chain structures or doublezig-zag structures. Upon cooling, an anomaly appears in theresistivity and magnetic susceptibility at Tc ∼ 170 K whichcoincides with the formation of a modulated structureaccording to x-ray diffraction [10,15]. Pressure and Sesubstitution were found to destabilize the modulation infavor of superconductivity [17–19]. In the quest to visualizethe local structure, scanning tunneling microscopy (STM)was used to image the high temperature (HT) phase and lowtemperature (LT) phase on the surface. Striped contrast in theHT phase was proposed to represent chains of Ta dimersinstead of trimers [20], however, the stripes are alsoconsistent with the surface Te atoms undergoing the bulkdistortion [21,22]. Mapping the bulk structure and disen-tangling lattice displacements from charge modulations arethus required for resolving the nature of density waves in1T 0-TaTe2 and layered TMDs in general [23–25].In high-angle annular dark-field (HAADF) scanning

transmission electron microscopy (STEM), 2D projectionimages of atomic column positions can be obtained at sub-angstrom resolution, even under cryogenic conditions[26,27]. Previously, we mapped the superstructure in acharge-ordered manganite at low temperature by directly

Published by the American Physical Society under the terms ofthe Creative Commons Attribution 4.0 International license.Further distribution of this work must maintain attribution tothe author(s) and the published article’s title, journal citation,and DOI.

PHYSICAL REVIEW LETTERS 125, 165302 (2020)

0031-9007=20=125(16)=165302(6) 165302-1 Published by the American Physical Society

measuring the picoscale PLD of atomic columns [27]. Inthat particular system, both the atomic structure and thedisplacements were aligned coherently along the viewingdirection. Layered materials present additional challengessince the superstructures may exhibit periodic and stag-gered out-of-plane stacking sequences or even disorderedstacking. These interlayer orders are increasingly pertinentfor understanding and manipulating the electronic groundstates of layered systems [28–30]. The patterns of displace-ments in the superstructures may, however, be obfuscatedby their stacking sequences, requiring atomic-scale probesand new methods that can reveal these distortions.Here we perform cryogenic HAADF-STEM measure-

ments to visualize the atomic-scale structure of the HT andLT phases in 1T 0-TaTe2. We first confirm that the HT phaseinvolves trimer distortions of Ta sites in agreement withearlier refinements of the bulk structure [9,15]. In the LTphase, we observe the formation of a threefold super-structure, which appears as periodic intensity modulationsin STEM data. While this LT transition is concealed incross section [31], analysis of the pattern of the intensitymodulations in plan view achieves a real space visualizationof the displacement pattern, consistent with an additionaltrimerization along the b axis. A combination of densityfunctional theory (DFT) calculations and image simula-tions confirms the effects of lattice distortions and theirstaggered stacking on STEM image contrast in plan view,enabling atomic-scale imaging of transitions with complexlattice order.Plan-view samples are prepared by exfoliating commer-

cial bulk crystals (HQ Graphene) onto silicon nitride gridswith holes while cross-sectional samples are fabricatedusing focused ion beam [31,38]. Figures 1(a) and 1(b) showthe room temperature structural model and high-angleannular dark-field (HAADF) STEM image of 1T 0-TaTe2,viewed along the b axis of the monoclinic cell. The contrastin HAADF-STEM scales strongly with the atomic number,Z, so Ta columns (Z ¼ 73) appear bright and the Te(Z ¼ 52) columns are dimmer. When the crystal is orientedalong a high-symmetry axis, the electron probe can channelalong the atomic columns before scattering onto thedetector, which further affects the contrast between heavyand light columns [39].The room temperature 1T 0 structure appears highly

distorted compared to the 1T phase (space group P3̄m1)with one TaTe2 formula unit in the unit cell. The distortioninvolves displacements of two Ta columns towards a thirdstationary Ta column, forming trimerized clusters (whitebracket). The Ta-Ta column distance within a trimer isshortened while the intertrimer Ta-Ta bond distance iselongated. By measuring atomic column positions alongthis viewing direction, we find that the short [long] Ta-Tacolumn distance in projection is 2.76(5) Å [3.97(4) Å],which corresponds to Ta-Ta bond lengths of 3.30(6) Å[4.37(5) Å] [31]. We also observe attendant distortions of

tellurium atoms, particularly those that move towards thegap between neighboring trimers. Moreover, the trimerizedclusters are staggered between the layers, forming a three-layer repeat sequence (ABC stacking). Cross-sectionalimaging over larger fields of view does not reveal anyregions with AAA stacking or stacking faults, suggestingthat the interlayer ordering of the trimers is important [31].In STM visualizations of surface layers in tellurides,

distorted chain structures appear as periodic striped contrastreflecting both electronic and lattice contributions. Whilethe stripes were interpreted as Ta dimer chains by Fenget al. [20], the contrast more likely reflects the telluriumdistortions in the top layer which can occur in bothdimerized and trimerized states [22]. Complementingprevious refinements of the structure [15,21], our dataunequivocally shows that 1T 0-TaTe2 forms trimer distor-tions. Further, these trimers occur throughout the sampleincluding in the top layer of the film [40].In plan view, the Ta atoms are misaligned [Fig. 1(c)] due

to the ABC stacking of trimers whereas the Te atomsremain stacked on top of each other. Figure 1(d) shows theSTEM image at room temperature in which the Te columns

ac

b

a

c

(b)(a)

(d)(c)

1nm

1nm

Ta

Te A

B

C

a

c

b

a+2c

FIG. 1. (a),(b) Room temperature structural model andHAADF-STEM image of 1T 0-TaTe2, respectively, viewed incross section and along the b direction of the monoclinic cell. Theunit cell is marked by dashed lines. The white brackets delineatetrimerized clusters of Ta atoms. (c),(d) Structural model andHAADF-STEM image in plan view at 293 K. The Te atomsappear bright and round while Ta atoms appear elongated anddimmer.

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appear round and the Ta columns appear elongated [41].The elongation, which occurs in the direction perpendicularto the b axis, reflects the projection nature of STEM.Furthermore, despite having a larger atomic number, Tacolumns are now dimmer than Te columns. In STEM, thepresence of imperfections along the beam direction, such asatomic displacements or chemical disorder, may cause theprobe to de-channel leading to measurable changes in thescattered intensity [39,42–45]. The dramatic reduction inTa column intensity is a direct illustration of how STEMcontrast can be sensitive to the 3D arrangement of distortedclusters.Figures 2(a) and 2(b) show plan-view images at room

temperature and at 93 K, respectively. Before inspecting thereal space data, the presence of a modulated structure at lowtemperature can be confirmed by comparing Fourier trans-forms (FTs) of the two images. Figure 2(c) shows the FTamplitude in the HT phase, where the Bragg peaksassociated with the crystalline lattice are visible. The FTamplitude of the LT STEM image [Fig. 2(d)] reveals thepresence of superlattice peaks (blue circles). The in-planesuperlattice wave vector amplitude is q ¼ 1=3 reciprocallattice units (r.l.u.) [Fig. 2(d), inset], indicating the for-mation of a threefold superstructure.The raw STEM data itself show structural distortions at

low temperature. The inset in Fig. 2(a) shows a zoomed-in

image at room temperature which exhibits the elongation ofTa columns in the HT phase. Upon cooling, additionaldeformations are observed in the shapes of Ta columns. Twoout of three Ta columns exhibit moon-shaped distortions,pointing towards a third undistorted Ta column. By con-sidering the projection nature of STEM, the data indicatesthat a fraction of Ta atoms in the distorted columns haveshifted towards the central Ta site. In the cross-sectionalorientation viewed along the b axis [as done in Fig. 1(a)], nosuperlattice is visible at low temperature. On the other hand,a low temperature superlattice is detected in the cross-sectional view with the b axis aligned perpendicular to thebeamdirection. Nevertheless, this does not reveal the patternof distortions because the displacements stack in a compli-cated fashion, necessitating alternative approaches to extractdetailed information in plan view [31].Ideally, we would like to directly measure the displace-

ments of individual columns, however, the projection natureof STEM requires coherent stacking of both the atomsand their displacements. For the more complex atomicarrangement in 1T 0-TaTe2, atom tracking approaches willtherefore fail. To overcome this limitation, we insteadanalyze HAADF contrast variations which arise from thesensitivity of electron beam channeling to distortions in thelattice. The intensity modulations in the image can beextracted by comparing the LT image, IðRÞ, to a reference,unmodulated lattice image, IrefðRÞ. We generate suchreference image by damping the amplitude of the super-lattice peaks in the FT to the background level and applyingan inverse FT [27,46]. The resulting IrefðRÞ has no periodiccomponent associated with q ¼ 1=3 r:l:u:. We note thatIrefðRÞ does not exactly correspond to the HT phase sinceother distortionmodes with different periodicity that may bepresent remain in the image [47].By subtracting the reference lattice image [Fig. 3(b)]

from the raw image [Fig. 3(a)], we obtain an intensity map[Fig. 3(c)] which encodes the real space pattern of theintensity modulation at low temperature. The green (brown)pixels represent an increase (decrease) in HAADF intensityat low temperature. The threefold superstructure (blackbracket) emerges from periodic variations in the intensity ofthe STEM image [Fig. 3(e)].Focusing on Ta columns (black dots), we observe three

kinds of intensity modifications. The first appears as adumbbell and involves a decrease of the intensity on the leftside of the Ta column and an increase on the right [Fig. 3(d)].The second, a mirror of the first, involves a decrease ofthe intensity on the right side of the Ta column and anincrease on the left [Fig. 3(d)]. The intensity redistribution ofTa-1 (Ta-3) is consistent with longitudinal displacements ofTa atoms to the right (left) along the b axis (in themonocliniccell). On Ta-2 columns, the change in intensity is smallerand is consistent throughout the field of view [31]. However,it is not easily interpretable in terms of lattice displace-ment or stacking disorder. Together, the low temperature

(a) (b)

(c) (d)F

T a

mpl

itude

0 1/3 12/3

293 K 93 K

b* b*

1 nm 1 nm

ba+

2c

-4(a+2c)* -4(a+2c)*

b

a+2c

FIG. 2. (a),(b) STEM image at 293 K and 93 K, respectively.The insets show zoomed-in views of the images, over a ∼1 nm ×1 nm field of view. (c),(d) Amplitude of the Fourier transform(FT) at 293 K and 93 K. The inset shows linecuts of the FTamplitude from (c) (red) and (d) (blue) along the b� direction. Atlow temperature, in-plane superlattice peaks (blue circles) withq ¼ 1=3 reciprocal lattice units appear in the FT, reflecting thepresence of a modulated structure.

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displacement pattern on the Ta columns may be viewed as anadditional trimerization along the b axis [10,15].The superstructure also contains periodic intensity mod-

ulations on the Te sites. In particular, the Te columns whichflankTa-2 columns have lower intensity, which indicates thatthe stacking of Te atoms is more distorted in the LT phase.Such tellurium distortions can dramatically affect the elec-tronic behavior of MTe2 systems by modulating the inter-layer bonding network [6]. TheTe sites surroundingTa-1 andTa-3 columns show negligible changes in STEM intensity.We next confirm the real space displacement pattern by

comparing toDFTstructural optimization.Weuse theViennaab initio simulation package (VASP) [48] code with projectoraugmented waves [49] and the PBEsol exchange-correlationfunctional [50] which is known to yield accurate equilibrium

structural parameters. Starting from the 1T phase of TaTe2(spacegroupP3̄m1),we computedphonon frequencies usingthe supercell frozen-phonon approach [31] and found 18displacement modes with imaginary frequencies, whichindicates that the 1T phase is unstable and may lower itsenergy by condensing combinations of these displacements.Both the HT and the LT phase were found to have lowerenergy. Analysis of the two crystal structures shows that theHT-LT transition involves longitudinal Ta displacements inthe Ta-1 and Ta-3 columns which may be described as atrimerization along the b direction, in agreement with the LTdistortion measured in the STEM data and in previousstructural refinements [10,15]. The transition also involvesTe distortions as well as zone-center modes. Remarkably, thedifference in energy of the two structures is small despite thelarge structural distortions in theLTphase.Moredetails aboutthe DFT methodology, symmetry analysis, and atomicpositions are given in the Supplemental Material [31].To firmly establish the link between these lattice dis-

tortions and STEMcontrastmodulations at low temperature,we perform multislice simulations on the DFT-optimizedstructures. In addition to simulating fully relaxed structures,we simulated images with only Ta or Te displacements, toassign displacement patterns to specific contrast features inthe data [31]. Figure 4(b) shows the calculated STEM imagein the HT phase, where we observe bright, round telluriumcolumns and the elongation of tantalum columns, in accor-dance with the experimental data. The calculated STEMimage based on the fully relaxed LT structure is shown inFig. 4(c) and the difference between theHTand LT images isshown in Fig. 4(d). The LT trimerized distortion appears as adeformation of the shape of Ta columns along the b axis. Inthe difference image, the distortion generates the dumbbell-shaped intensity patterns on Ta-1 and Ta-3 columns.The Ta-2 columns exhibit negligible changes in the

contrast whereas the experimental data shows a smallchange in intensity. The minor discrepancy might reflectthe fact that IrefðRÞ does not exactly correspond to the HTphase since other modes present in the structural transitionare not captured by the q ¼ 1=3 r:l:u: Fourier components[47]. Alternatively, experimental imperfections such ascrystal mistilt, aberrations, or surface damage may accountfor the difference. That said, the dominant LT contrastmodifications on Ta sites are well explained by a trimeriza-tion along the b direction. For tellurium columns, both theLT image and the difference image show a reduction inSTEM intensity only on the Te sites flanking the Ta-2column (white crosses), reflecting the variations observed inthe experimental data. Based on the atomic positions in theLT phase, the decrease in STEM intensity on those Tecolumns is a result of a less coherent stacking of the atoms.By comparing image simulations and experimental intensitymodulations in plan view, we therefore achieve a visuali-zation of not only the Ta trimerization but also the moresubtle Te distortions in the LT phase of 1T 0-TaTe2.

(a)

(d)

(b) (c)

(e)

FIG. 3. (a) Section of the low temperature (LT) STEM image,IðRÞ, spanning a projection of the monoclinic unit cell. (b)Generated reference image, IrefðRÞ, of the same field of view, asdescribed in the text. Black dots represent Ta columns and crossesrepresent Te columns. (c) Difference map between IðRÞ andIrefðRÞ. The map encodes the modulations in STEM contrastwhich are responsible for the superlattice peaks. The bracketdelimits a single low temperature trimerized cluster. Whitecrosses represent Te atomic columns that show a reduction inintensity. (d) Zoom-in on the Ta-1, Ta-2, and Ta-3 columns andtheir respective intensity modifications. (e) Large field of view ofthe difference map showing periodic intensity modulations. TheLT unit cell is marked by the dashed lines.

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Probing the bulk structure in layered systems is impor-tant for understanding the electronic properties of nomi-nally quasi-2D TMD systems. While interlayer interactionsare prominent in MTe2 compounds, recent studies on1T-TaS2, a prototypical 2D CDW system, also suggestthat the out-of-plane ordering of CDW clusters may beresponsible for its insulating ground state and its exotic,metastable phases [30]. These interlayer structures, how-ever, have proven difficult to visualize at atomic resolution[24,29]. As demonstrated here, mapping contrast modifi-cations in cryogenic STEM enables the visualization ofphase transitions with complex displacement patterns.

This work was supported by the National SciencesFoundation (NSF) through the Platform for theAccelerated Realization, Analysis, and Discovery ofInterface Materials (DMR-1539918), and made use ofthe shared facilities of the Cornell Center for MaterialsResearch with funding from the NSF MRSEC program(DMR-1719875). Assistance provided by G.M. S. in thepreparation of samples was funded by the US Departmentof Energy (DE-SC0017671). The FEI Titan Themis 300was acquired through NSF-MRI-1429155, with additionalsupport from Cornell University, the Weill Institute, and theKavli Institute at Cornell.

*Corresponding author.lena.f.kourkoutis@cornell.edu

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(a) (b) (c) (d)

FIG. 4. (a) Low temperature structure obtained from DFT structural optimization. Tantalum atoms within the existing HT trimersundergo longitudinal periodic lattice displacements along the b axis, forming additional trimerized clusters. More subtle telluriumdisplacements occur as well. The dashed box delimits the simulated field of view. (b),(c) Multislice simulation of HAADF-STEMimages of the HT and LT phase, respectively. The dots represent Ta columns and the crosses represent Te columns. The dashed lineshighlight distortions in the Ta columns (Ta-1 and Ta-3) at low temperature. (d) The difference image shows a periodic intensitymodulation that emerges at low temperature. The bracket delimits the low temperature Ta trimers and the white crosses represent Tecolumns that exhibit a reduction in intensity.

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